Fig. 2: Behaviour of a minimal modification motif.

a The motif includes two states of A, unphosphorylated (A-{0}) and phosphorylated (A-{P}). The motif contains four different reaction types: component A can be synthesised (in its neutral state A-{0}), degraded (in either state), phosphorylated (consumes A-{0}, produces A-{P}) or dephosphorylated (consumes A-{P}, produces A-{0}). The regulatory and elemental species-reaction graphs of the motif can be found in Supplementary Fig. 1. b–d Initial conditions, expectations and simulation results. Each line correspond to the simulation of one or more model variants, and visualise which reactions are active, which states are initiated, which behaviour we expect, and the behaviour we observed. b To define the desired behaviour of the motif, we create 64 variants of the motif with each of the four reactions constitutively ON (true) or OFF (false) (columns 1–4), and each of the elemental states initially true or false (columns 5 and 6), and define the expected steady state as a function of initial state and active reactions (“Expected attractor”; columns 7 and 8). (I) In the absence of any reactions, the steady state will be identical to the initial state. (II–III) In the absence of synthesis or degradation, but in the presence of component A (A-{0} or A-{P} true), the equilibrium depends on the (de)phosphorylation reactions. With only one of these reactions, only the fully (de)phosphorylated form is present at steady state. However, with both reactions present we expect both elemental states to be present at steady state. (IV) With degradation but not synthesis active, the protein will be depleted and both states will be false at steady state. (V) With active synthesis, the neutral state will always be present. The phosphorylated state will only be present if there is also a phosphorylation reaction or if the state is initially present and both the degradation and dephosphorylation reactions are off. c The attractors reached after simulation with the update rules in the original ansatz. The attractors correspond to the expected attractors (see B) for 62 out of 64 configurations. The exception are the cyclic attractors in block (III), where both phosphorylation and dephosphorylation are active and only one of the elemental states are initiated as true. d The attractors reached after simulation with the smoothed update rules. The attractors are identical to the expected attractors in all cases.